Alter Web Portal searching capability based on logged in user

Hello,

    Looking to see if it is possible to restrict who can search who on the web portal. As of right now by default it seems it is configured that anyone can search up anyone. An example would be that only managers should be able to find results on a larger variety of people(people they manage or other managers) verse someone that is not a manager should not be able to search up someone higher up in the chain of command. Is something like this possible?